Answer:
y(x) = 7e^(5x)
Step-by-step explanation:
The question says that the slope of the curve at every point P is five times the y-coordinate of P. This means that
dy/dx = 5y
Refer to solutions of differential equations, dy/dt = ky, being in the form of y(t) = y(0) e^(kt)
Using the above stated law now, we can relate to our equation, saying that
y(x) = y(0) e^(5x)
The point given from the question is, (0, 7). This also means that y(0) = 7. So finally, we can have
y(x) = 7e^(5x)
And that is our needed equation of the curve
The difference is that evaluating an expression for a given value is an example of let’s say In a example, the variable x is equal to 6 since 6 + 6 = 12. So it means that they are giving you the input already. SOLVING an equation is working backwards, to undo everything that has been done to the input. So you have to do the equation in order to find your answer.
1) The variables are "k"
2) There are 4 terms
3) The coefficients are k
4) The constants are -7, 3, 10, -5
5) The like terms is -7k, 3k, 10k, -5k
The answers are pretty direct but, hope this answers your question.
Have a great day/night!
The third choice is the correct choice.
